TITLE: Does the function $\log(1+\exp(x))$ have a conventional name?
QUESTION [6 upvotes]: Does the function $\log(1+\exp(x))$ (or the function $\log(1+\exp(-x))$) have a conventional or at least fairly common name?
Alternatively, is it closely related to some reasonably well-known, named function? 
[It arises in a problem I'm working on and it would be nice to use a reasonably standard terminology and notation rather than either writing $\log(1+\exp(g(x)))$ each time (where $g$ is a fairly complicated set of terms), or coming up with a non-standard notation for it (like $\omega(g(x))$ say) and then discovering I could have used a symbol and term for it that are already recognized). It would also help in terms of locating properties, should I end up needing any beyond the simple ones I've already derived.]

REPLY [7 votes]: The name softplus has been coined in 2001 (Dugas et al.), and seems to be in fairly common use by now.